There is a standard connector which existed before big screens landed in cars, the OBD2 connector. Dongles are cheap and you can read the output from your phone or computer. Some dongles support bluetooth. The connector is mandated in some markets and I guess that makes it less interesting to add a redundant interface inside of the car. It’s fun to try if you’re interested. Manufacturers can extend the error codes IIRC.
Tesla has a service mode on the display through which you can scan the car for faults, run a battery test, … It is password protected but the password is publicly available.
Updated my comment to reflect this. Thanks for clearing out the confusion.